ترغب بنشر مسار تعليمي؟ اضغط هنا

On the spaces of bounded and compact multiplicative Hankel operators

97   0   0.0 ( 0 )
 نشر من قبل Karl-Mikael Perfekt
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

A multiplicative Hankel operator is an operator with matrix representation $M(alpha) = {alpha(nm)}_{n,m=1}^infty$, where $alpha$ is the generating sequence of $M(alpha)$. Let $mathcal{M}$ and $mathcal{M}_0$ denote the spaces of bounded and compact multiplicative Hankel operators, respectively. In this note it is shown that the distance from an operator $M(alpha) in mathcal{M}$ to the compact operators is minimized by a nonunique compact multiplicative Hankel operator $N(beta) in mathcal{M}_0$, $$|M(alpha) - N(beta)|_{mathcal{B}(ell^2(mathbb{N}))} = inf left {|M(alpha) - K |_{mathcal{B}(ell^2(mathbb{N}))} , : , K colon ell^2(mathbb{N}) to ell^2(mathbb{N}) textrm{ compact} right}.$$ Intimately connected with this result, it is then proven that the bidual of $mathcal{M}_0$ is isometrically isomorphic to $mathcal{M}$, $mathcal{M}_0^{ast ast} simeq mathcal{M}$. It follows that $mathcal{M}_0$ is an M-ideal in $mathcal{M}$. The dual space $mathcal{M}_0^ast$ is isometrically isomorphic to a projective tensor product with respect to Dirichlet convolution. The stated results are also valid for small Hankel operators on the Hardy space $H^2(mathbb{D}^d)$ of a finite polydisk.



قيم البحث

اقرأ أيضاً

186 - Yiyuan Zhang , Guangfu Cao , Li He 2021
In this paper, we investigate the boundedness of Toeplitz product $T_{f}T_{g}$ and Hankel product $H_{f}^{*} H_{g}$ on Fock-Sobolev space for two polynomials $f$ and $g$ in $z,overline{z}inmathbb{C}^{n}$. As a result, the boundedness of Toeplitz oper ator $T_{f}$ and Hankel operator $H_{f}$ with the polynomial symbol $f$ in $z,overline{z}inmathbb{C}^{n}$ is characterized.
179 - Jordi Pau 2015
We completely characterize the simultaneous membership in the Schatten ideals $S_ p$, $0<p<infty$ of the Hankel operators $H_ f$ and $H_{bar{f}}$ on the Bergman space, in terms of the behaviour of a local mean oscillation function, proving a conjecture of Kehe Zhu from 1991.
123 - Thomas Kalmes 2020
We study topologizability and power boundedness of weigh-ted composition operators on (certain subspaces of) $mathscr{D}(X)$ for an open subset $X$ of $mathbb{R}^d$. For the former property we derive a characterization in terms of the symbol and the weight of the weighted composition operator, while for the latter property necessary and sufficient conditions on the weight and the symbol are presented. Moreover, for an unweighted composition operator a characterization of power boundedness in terms of the symbol is derived for the special case of a bijective symbol.
A pair of functions defined on a set X with values in a vector space E is said to be disjoint if at least one of the functions takes the value 0 at every point in X. An operator acting between vector-valued function spaces is disjointness preserving if it maps disjoint functions to disjoint functions. We characterize compact and weakly compact disjointness preserving operators between spaces of Banach space-valued differentiable functions.
111 - Thomas Kalmes 2018
We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted) composition o perators are power bounded, topologizable, and (uniformly) mean ergodic on kernels of certain linear partial differential operators including elliptic operators as well as non-degenrate parabolic operators. Moreover, under mild assumptions on the weight and the symbol we give a characterisation of those weighted composition operators on the Frechet space of continuous functions on a locally compact, $sigma$-compact, non-compact Hausdorff space which are generators of strongly continuous semigroups on these spaces.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا